Sparse Constrained Manifold Regularized Concept Factorization Algorithm

Manifold learning algorithms assumed that the observed data are sampled from a smooth manifold, while the actual high-dimensional data often exist noise or outliers due to various factors. The concept factorization（CF） algorithm cannot deal with the noise effectively and capture the intrinsic geometrical structure simultaneously. In this paper, a novel algorithm called sparse constrained manifold regularized concept factorization（SMCF） is proposed, which using l_2,1 norm incorporated in the objective function of concept factorization to obtain the feature vectors with more discriminating ability, and extract the intrinsic manifold structure of samples by constructing graph Laplacian regularizer to improve the discrimination power. The objective function of SMCF is solved by the iterative multiplicative updating algorithm and its convergence is also proved in this paper. The experimental results on PIE, AT＆T, Reuters and TDT2 datasets have shown that the proposed approach achieves better clustering performance in terms of accuracy and normalized mutual information.